Question

Determine the coordinates of the image if triangle ABC is translated 6 units down.

A′(−5, −2), B′(3, −2), C′(−1, 2)
A′(1, 4), B′(9, 4), C′(5, 8)
A′(1, −8), B′(9, −8), C′(5, −4)
A′(7, −2), B′(15, −2), C′(11, 2)

Answer 1

To translate a point downwards, you subtract from the y-coordinate of each point. In this case, the triangle is being translated 6 units down.

Let's analyze the coordinates provided:

1. A′(−5, −2), B′(3, −2), C′(−1, 2)
2. A′(1, 4), B′(9, 4), C′(5, 8)
3. A′(1, −8), B′(9, −8), C′(5, −4)
4. A′(7, −2), B′(15, −2), C′(11, 2)

For each option, apply the translation:

**1. A′(−5, −2), B′(3, −2), C′(−1, 2)**
- A′: (-5, -2 - 6) = (-5, -8)
- B′: (3, -2 - 6) = (3, -8)
- C′: (-1, 2 - 6) = (-1, -4)

**Result**: A′(-5, -8), B′(3, -8), C′(-1, -4)

**2. A′(1, 4), B′(9, 4), C′(5, 8)**
- A′: (1, 4 - 6) = (1, -2)
- B′: (9, 4 - 6) = (9, -2)
- C′: (5, 8 - 6) = (5, 2)

**Result**: A′(1, -2), B′(9, -2), C′(5, 2)

**3. A′(1, −8), B′(9, −8), C′(5, −4)**
- A′: (1, -8 - 6) = (1, -14)
- B′: (9, -8 - 6) = (9, -14)
- C′: (5, -4 - 6) = (5, -10)

**Result**: A′(1, -14), B′(9, -14), C′(5, -10)

**4. A′(7, −2), B′(15, −2), C′(11, 2)**
- A′: (7, -2 - 6) = (7, -8)
- B′: (15, -2 - 6) = (15, -8)
- C′: (11, 2 - 6) = (11, -4)

**Result**: A′(7, -8), B′(15, -8), C′(11, -4)

Now we compare these results to determine the correct set of coordinates after the translation:

The only set of coordinates that match is:
**Result from 1.** A′(-5, -8), B′(3, -8), C′(-1, -4)

So, the correct answer is none of the listed options.

If the question intended for us to select from the given options, the closest option that follows the vertical translation by 6 units down will not satisfy as shown above. Thus, we should clarify the options listed with respect to the translation direction to ensure alignment.